In a small saucepan combine wine or grape juice, sugar, and fresh ginger. Bring to boiling; reduce heat. Simmer, covered, for 5 minutes. Remove from heat. Strain ginger from mixture. Discard ginger. Cover and chill for 2 to 24 hours.
Before serving, in a medium mixing bowl combine cantaloupe, honeydew, and wine or juice mixture. Toss gently to coat. To serve, divide mixture evenly among 6 cups or bowls. Garnish with strips of crystallized ginger, if desired. Makes 6 servings.